Modeling joints with multiple members in Hencky bar-chain model for buckling analysis of frames

Comprising rigid segments connected by hinges with elastic rotational springs, the Hencky bar-chain model (HBM) has some advantageous features over traditional structural models in that it can handle local structural changes easily and allows easy coding for analyses. The development of the HBM was previously rather limited to structural members and simple frames. Continuing along the development of an HBM for bifurcation in-plane buckling analysis of frames, a new connection model is proposed herein to handle joints receiving multiple members that are encountered in multi-bay-multi-storey frames. The connection stiffness matrices associated with the elastic strain energies of the deformed multi-member connection are formulated. The connection stiffness matrices together with the elastic stiffness and geometric stiffness matrices for members are readily coded in a computer program—HBM solver for elastic bifurcation in-plane buckling analysis of frames, and the MATLAB code is given in the Appendix. The HBM with the new connection model is verified by comparing its results with frame buckling loads and mode shapes obtained from the traditional matrix stiffness method involving stability functions. The advantages of the HBM over traditional structural models are also demonstrated, including its simplicity in handling non-uniform cross-sectional members.